The age-hardenable Al-Mg-Si alloy system is strengthened by needle-shaped coherent β'' phase precipitates. Using distortion-corrected high-resolution scanning transmission electron microscopy images, we measure the considerable misfit between β'' particles and the Al matrix. The β'' phase is found to adapt its lattice parameters to the particle shape, distributing the strain in the Al matrix evenly in its cross-sectional plane. The measured misfits give a good match to reported atomistic simulations for a β'' phase with composition Mg5Al2Si4.Keywords: electron microscopy, aluminium alloys, precipitation, misfit strain 2 Coherent precipitates in age hardenable alloys and the misfit strain fields they induce in the surrounding matrix have been text book material for many decades [1]. Such precipitates form by thermally activated diffusion, nucleation and growth. A precipitate particle stays coherent until it grows too large for the matrix to accommodate all its misfit. After this, precipitates experience a loss of coherency, and the strain fields diminish, weakening the material. This can happen through several mechanisms:(i) a phase transformation to a less coherent phase (ii) formation of an incoherent surface layer at the matrix-precipitate interface (iii) introduction of interface (misfit) dislocations The precipitate phase can also relieve the system of some strain before coherency loss occurs by less drastic modifications:(iv) generation of stacking faults in the precipitate phase (v) chemical adjustments, including an increased vacancy density in or outside the precipitate phase All five effects can be studied using theoretical calculations such as density functional theory (DFT) or continuum mechanics through the finite element method (FEM). However, calculations need support by experiments at the atomic scale. Experimental studies require that we can both observe the causes (e.g. a single stacking fault) and quantify the resulting change in lattice strain. It is equally important to ensure the absence of faults, if the strain around a perfectly coherent particle is of interest.In this study, we focus on measuring the misfit of perfectly coherent β'' precipitates of the Al-Mg-Si system [2-4] through scanning transmission electron microscopy (STEM). This phase is described by the monoclinic C2/m space group and was initially thought to have composition Mg5Si6, but Mg5Al2Si4 is probably closer to the truth [5,6]. Its lattice parameters have been measured to a = 1.516 nm, b = 0.405 nm, c = 0.674 nm, and its monoclinic angle is 105.3° [2,3]. The phase was chosen since it is one of few fully coherent phases in aluminium alloys, and the main hardening phase of an industrially important alloy system. It is also needle-shaped with a long main coherency direction, often extending through the TEM specimen in which it resides. The lattice strain is therefore uniform through the specimen, and can be measured reliably in a projected image of a precipitate cross-section.When corrected for spherical aberratio...